Endpoint distribution of directed polymers in 1+1 dimensions
arXiv:1106.2716 · doi:10.1007/s00220-012-1583-z
Abstract
We give an explicit formula for the joint density of the max and argmax of the Airy process minus a parabola. The argmax has a universal distribution which governs the rescaled endpoint for large time or temperature of directed polymers in 1+1 dimensions.
Expanded introduction
References in corpus (7)
- Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
- Non-intersecting Brownian walkers and Yang-Mills theory on the sphere
- Exact distribution of the maximal height of p vicious walkers
- A determinantal formula for the GOE Tracy-Widom distribution
- Continuum statistics of the Airy2 process
- Local behavior and hitting probabilities of the Airy1 process
- The One-dimensional KPZ Equation and the Airy Process
Cited by in corpus (19)
- Extreme value statistics of correlated random variables: a pedagogical review
- Airy processes and variational problems
- Local behavior and hitting probabilities of the Airy1 process
- Continuum statistics of the Airy2 process
- On the joint distribution of the maximum and its position of the Airy2 process minus a parabola
- Transversal fluctuations of the ASEP, stochastic six vertex model, and Hall-Littlewood Gibbsian line ensembles
- On global solutions of the random Hamilton-Jacobi equations and the KPZ problem
- Revisiting Directed Polymers with heavy-tailed disorder
- Limiting distribution of maximal crossing and nesting of Poissonized random matchings
- Multiplicative functionals on ensembles of non-intersecting paths
- Non-intersecting Brownian bridges and the Laguerre Orthogonal Ensemble
- Tails of the endpoint distribution of directed polymers
- Supremum of the Airy2 process minus a parabola on a half line
- Crossing probability for directed polymers in random media: exact tail of the distribution
- Distribution function of the endpoint fluctuations of one-dimensional directed polymers in a random potential
- Midpoint distribution of directed polymers in the stationary regime: exact result through linear response
- Tail decay for the distribution of the endpoint of a directed polymer
- Power countings versus physical scalings in disordered elastic systems - Case study of the one-dimensional interface
- A PDE hierarchy for directed polymers in random environments